Blog page on a separate domain

Yes, It can be possible.
Best way is by using wordpress multisite. For that, you need to create a network.

Other way around this problem, is by using URL Cloaking or Redirects [Ususally found in domains section]. You need to redirect https://www.mysite.com/blog to https://www.blogatmysite.com/

Best way is by using wordpress multisite.

Original post mentioned “Not Multisite”.

You have to make sure that every request to https://www.blogatmysite.com/* is being redirected to https://www.mysite.com/blog/*

I’m not an expert on this, but I believe some regex expressions and rewrite rules (or redirect rules) in your .htaccess file will help.

I believe something like this:

Options +FollowSymLinks -MultiViews
RewriteEngine On
RewriteBase /

RewriteCond %{HTTP_HOST} ^(www\.)?blogatmysite.com$ [NC]
RewriteRule ^ https://www.mysite.com/blog%{REQUEST_URI} [L,NE,P]

You’ll have to make sure that the new domain points to the same domain as the old site though.

(untested code, but give it a try and see!)